In the Reform High Holiday services we repeat
several times that it is not the death of sinners that G-d wants,
but that they should turn away from their unholy ways (this may
be part of the Orthodox and/or Conservative services, too). Is
there any scriptural basis for that statement, or is it just part
of the prayer writers' rhetoric? If there is scriptural basis,
it seems to me that it would be a good rebuttal to those who claim
that capital punishment is Biblically mandated.

Dear Saul "The Maven" Caplan,

The phrase you mentioned is from a verse in Yechezkel
(Eziekiel 33:11). In context, this passage doesn't contradict
the Biblical death penalty but rather supports it.

Here's the context: In the previous verses (7-10)
G-d tells the Prophet Yechezkel to warn the wicked people to repent
or die; if Yechezkel fails to warn them then he will be blamed
for their death, but if he does warn them, then their death will
be their fault. Why? Because "I don't desire the death
of the wicked person; but rather that he return from his ways
and live." That is, the death penalty is not that G-d wants
revenge, but rather it is a warning to repent before it's
too late. (This shows the danger of taking an isolated verse
without studying the context.)

The Biblical death penalty is mentioned explicitly
several times throughout the Torah, however it was very rarely
performed (less than once every 70 years).